Friday, 2 May 2014

`int (x^3 - 2sqrt(x))/x dx` Find the general indefinite integral.

Given `int((x^3-2sqrt(x))/x)dx`


Simplify the expression by dividing each term by x.


`=int(x^2-2x^(-1/2))dx`


Integrate each term.


`=(x^3/3)-(2x)^(1/2)/(1/2)+C`


Simplify.


`=(x^3/3)-4x^(1/2)+C`


`=(x^3/3)-4sqrt(x)+C` 


Given `int((x^3-2sqrt(x))/x)dx`


Simplify the expression by dividing each term by x.


`=int(x^2-2x^(-1/2))dx`


Integrate each term.


`=(x^3/3)-(2x)^(1/2)/(1/2)+C`


Simplify.


`=(x^3/3)-4x^(1/2)+C`


`=(x^3/3)-4sqrt(x)+C` 


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